A Belief Propagation-Based Tree-EP Algorithm for MIMO Detection With High-Order Constellations

Multiple input multiple output (MIMO) technology that has been broadly applied necessitates detectors with high performance and low complexity. The detection problem becomes severe when a large scale of antennas is employed, and a variety of approaches have been proposed to deal with this problem among which expectation propagation (EP) proves to be able to perform efficient detection, especially for high-order constellations. However, the traditional EP algorithm treats all variables in an independent way, making it unable to exploit additional relations among symbols that are useful for further potentials in improving the detection performance. Therefore, we propose to utilize the Tree-EP framework that introduces pairwise approximations for variables on a constructed tree graph. Following the Tree-EP paradigm, three algorithms are proposed among which a belief propagation (BP) based Tree-EP algorithm is of significant effectiveness. It can be proved in theory that the solution of the BP based Tree-EP algorithm is a fixed point of Bethe free energy, leading to guaranteed convergence by effective message passing. Simulation results demonstrate that the BP based Tree-EP outperforms EP in both canonical and massive MIMO systems with complexities of the same order.